Volumetrics data into mesh
It is possible to get sharp defined edges using volumetrics - see Give this mesh a uniform thickness on all the tubes and unions. Assuming your source data is to sufficient resolution then it should just be a matter of adjusting the Volume Sampling settings in the Render properties. 



Decrease the Step Size to get better resolution. This is defined in blender units so pick a value that is close to the resolution of your data based on the size of the volume. If the number of steps does not span the volume then increase Max Steps to compensate.